Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces

Jason Bentley

Published: 2022-03-22
Language: EN

Vol. 36 No. 1 (2022)

Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces

Jason Bentley

Abstract

This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set functions defined recursively on an ascending sequence of rings of subsets with a set function limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a meticulous way to ensure that the set function limit is σ-additive.

(EN)

Keywords:

regular measure , non-atomic measure , strictly-positive measure , locally compact spaces , non-atomic spaces , Polish spaces , regular spaces , second-countable spaces (EN)

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Citation rules

Bentley, J. (2022). Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces. Annales Mathematicae Silesianae, 36(1), 15–25. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/13457

Vol. 36 No. 1 (2022)
Published: 2022-03-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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